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Omni-MATH / Two real numbers x and y are such that 8y⁴+4x²y²+4xy²+2x³+2y²+2x=x²+1. Find all possible values of x+2y².

Problem

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problem

Two real numbers xx and yy are such that 8y4+4x2y2+4xy2+2x3+2y2+2x=x2+18 y^{4}+4 x^{2} y^{2}+4 x y^{2}+2 x^{3}+2 y^{2}+2 x=x^{2}+1. Find all possible values of x+2y2x+2 y^{2}.
Plain-text mathematical notation (without MathML)
Two real numbers x and y are such that 8y⁴+4x²y²+4xy²+2x³+2y²+2x=x²+1. Find all possible values of x+2y².
Original LaTeX notation
Two real numbers $x$ and $y$ are such that $8 y^{4}+4 x^{2} y^{2}+4 x y^{2}+2 x^{3}+2 y^{2}+2 x=x^{2}+1$. Find all possible values of $x+2 y^{2}$.

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Source and history

task_id
8f54d081-857d-5af3-88c5-26ae8b1cc214
task_key
test--8f54d081-857d-5af3-88c5-26ae8b1cc214
task_revision_id
1
config / split
/ test

Official source

initial import